# math/physics

posted by .

a ball with mass 0.15 kg is thrown upward with initial velocity 20 m/sec from the roof of a building 30 m high. there is a force due to air resistance of |v|/30, where velocity v is measured in m/sec.
a. find the maximum height above the ground the ball reaches.
b. find the time the ball hits the ground.

you cannot use the kinematic equations.

• math/physics -

This IS a kinematics problem. Any equation used to solve it involves kinematics. An exact solution would require solving a (kinematic) differential equation.

A good approximation to part (a) can be obtained by assuming an average air resistance force of |V|/60 , where V is the initial velocity of 20 m/s. Thus work done against friction going up is
V/60*H, and initial kientic energy equals potential energy gain at the highest elevation PLUS work done against friction.
(1/2) M V^2 = M g H + V/60*H
H = (1/2)V^2/[g + V/(60M)]= (1/2)V^2/11
= 18.2 m

The time spent by the ball going up is
very nearly H/(V/2) = 0.46 s

Use a similar energy conservation argument to estimate the (longer) time it takes for the ball to come back down. Note that it must travel an additional 30 m to reach the ground.

• math/physics -

how would you solve it with differential equations

• math/physics -

Solve
M dv/dt = -M g -v/60*H
(v>0)

followed by
M dv/dt = -M g + v/60*H
(v<0)

Once you have v(t), integrate v dt to get the distance travelled vs t.

## Similar Questions

1. ### calc

a ball with mass 0.15 kg is thrown upward with initial velocity 20 m/sec from the roof of a building 30 m high. there is a force due to air resistance of |v|/30, where velocity v is measured in m/sec. a. find the maximum height above …
2. ### College algebra

When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -5t^2 + v*t + k gives the height of the ball at any time, t in seconds, where “v” is the initial velocity (speed) in meters/sec and “k” …
3. ### physics

A ball is thrown from the top of a building with an initial velocity of 30m/s straight upward, at an initial height of 50m above the ground. The ball just misses the edge of the roof on is way down and hits the ground. Determine: a) …
4. ### math

A ball is thrown from the edge of a cliff with an initial velocity of 60·m/s upward. Answer the following questions using + (upward) and - (downward) to indicate the direction of the velocity. Ignore air resistance and assume the …
5. ### Calculus Help

If a ball is thrown vertically upward from the roof of 64 foot building with a velocity of 32 ft/sec, its height after t seconds is s(t)=64+32t–16t2. What is the maximum height the ball reaches "in ft"?
6. ### Math

If a ball is thrown vertically upward from the roof of 48 foot building with a velocity of 80 ft/sec, its height after t seconds is s(t) = 48+80t-16t^2 What is the velocity of the ball when it hits the ground?
7. ### Math Calc

If a ball is thrown vertically upward from the roof of 48 foot building with a velocity of 112 ft/sec, its height after t seconds is s(t)=48+112t–16t^2. What is the maximum height the ball reaches "in ft"?
8. ### math-urgent

A ball with a mass 0.15kg is thrown upward with an initial velocity 20m/s from the roof of a building 30m high. Neglect air resistance. Find the max height above the ground that the ball reaches. Assuming the ball misses the building …
9. ### physics

A ball is projected upward at time t = 0 s, from a point on a flat roof 10 m above the ground. The ball rises and then falls with insignificant air resistance, missing the roof, and strikes the ground. The initial velocity of the ball …
10. ### Physics

A ball is thrown from the top of a building with an initial velocity of 30m/s straight upward, at an initial height of 50m above the ground. The ball just misses the edge of the roof on is way down and hits the ground. Determine: a) …

More Similar Questions